I finally discovered this video by Todd Jarrett
This guy is so full of hot air about law enforcement being 20 years behind in these techniques as to be laughable with regard to the grip or the stance. I learned to hold a pistol that way over 25 years ago from federal law enforcement firearms instructors and NRA instructors, and I taught holding it that way for about 14years. So unless this video is very old, I don't get the behind the times comment at all. Of course maybe he is just trying to sell "his" technique! The thing is many other people I know hold it that way and have been doing so for many years. Many instructors I know have been teaching that method for many, many years. There maybe slight, and I do mean slight, differences but it the same grip when it comes down to it. Now all of a sudden he has reinvented the wheel. What a good laugh that whole idea gave me if only because the firearms gurus always seem to be claiming something as their own that was being used many years before they thought of it, and the gurus repeat one another again and again and again, each one sort of claiming it as their own method.
As for the thumb, on the weak hand, it is not all as important as he makes it, I can train anyone, and I mean anyone to hold it almost straight up and they will shoot right on, though toward the target to a degree is more natural, though paralel to the index finger of the other hand is forcing it, but not by much.
One thing to be extremely careful of is that the thumb of the off side hand does not ride the slide, this can and definitely does lead to jamming in many cases. I have seen it over an over again, and then some.
As for this being a training film and the instructor allowing the guy to bring the pistol up the way he does, pointing it at about 45 degrees upinto the air then homing in on the target, shame on him for allowing very bad practice to be put into a training video. If you notice, the instructor does not once come on target lke that, and there is a reason not to do so because it takes more time, and it is a much less effective way of bringing a pistol to bear on target than punching or pushing it, or pointing it hard, forward toward the target.
All the best,
Glenn B